Hi - I noticed surface rust in the guttering, what should I treat it with to stop it getting worse?

Believe it or not Vaseline!! We had an elderly lady customer spread this on her Triumph Herald door because it was rusting and as Vaseline was water proof she thought it wood do the trick, we all just laughed.........Quite a number of years later when she sold the car and we bought it the rust wasn't any further forward
Don't use any water based stuff, it's not worth the bottle it comes in!
However there was a oil based product in New Zealand I used when I was there for many years and with excellent results, I just can't remember the name but came in an orange plastic container with black writing, it was also highly inflammable if you put it on and then welded before it was allowed to dry!
Failing that, sand back the surface to bare metal,prime and repaint and don't offer any water near the bare metal or your oily skin on the panel, all these impurities effect the paint longevity in the long term.

Our Triumphs do tend to suffer from paint loss in the actual guttering channel, and the primer can be seen underneath. I presume this is largely due to poor paint adhesion due in this area from manufacture. The result can be corrosion in the channel if left untreated. You don't need to remove the gutter trim unless the rust is excessive or the edge of the guttering has corroded. The trims are difficult to remove without damage, and equally difficult to refit, although with care it can be done. I would leave the trim if at all possible.
The good thing about it is that with a bit of care, some corrosion inhibitor can be applied by a thin brush, and then treated with primer and then colour. Where it is, paint applied by a thin brush (as long as the shade matches of course!) doesn't really look out of place, and it can be applied a little thicker because it is less likely to run, and it is covering spot welds which are uneven anyway. The only issue is if the rust has spread up onto the roof panel where a more in depth repair would be needed.